This how-to is written in such a way that (in my opinion) everybody, including people that are new to Linux/Freesco, can use it. This means that for more experienced users this how-to is probably too expansive. Sorry for that But I remember my first Freesco-days when I read howto's that I couldn't understand because it assumed the possession of basic skills which I didn't have at that time.
In this how-to, commands you'll have to input are in code blocks.

phpBB is a high powered, fully scalable, and highly customizable Open Source bulletin board package. phpBB has a user-friendly interface, simple and straightforward administration panel, and helpful FAQ. Based on the powerful PHP server language and your choice of MySQL, MS-SQL, PostgreSQL or Access/ODBC database servers, phpBB is the ideal free community solution for all web sites.
For more info take a look at the phpBB homepage: http://www.phpbb.com

Well, of course you'll need al working version of Freesco 03x, I'm using 0.3.3 myself. I'm running it on a Pentium 200MMX-64Mb, and that's enough to keep my small phpBB-forum running at acceptable speeds. Keep in mind that if you expect a lot of users you'll probably need a system that is a bit faster. Installing a PHP accellerator also helps a lot (at the expense of more RAM).
You also need a working Web server with PHP enabled. I use apache_1.3.27_dingetje-package with a kernel (I believe the 6th option) from the kernels-1.3-lightning-package. But you can also use a kernel from Dingetje's kernels page.
Another package you'll need is utils_1.0_dingetje. This package contains the tar command you'll need to untar the files you're about to download.
You'll also want a connection to your Freesco box using the standard Telnet-client or (better!!!) use SSH-access opensshd_3.7.1p1_dingetje-package.
I use putty.exe to connect to Freesco with my windows machine.
If you do not have all the packages required, download them at http://www.freescosoft.org or http://dingetje.homeip.net and install them ;)

Download the latest stable release of the phpBB2 forum software here: http://www.phpbb.com/downloads.php. This will eventually result in an URL from a Sourceforge mirror. Copy/paste that URL into the next snarf command (in the example below the Belgium mirror is used):

You'll notice that the files get unpacked in a new subdirectory called phpBB2. So, your forum is now located in /www/phpBB2
Now make your forum accessible to the web server (Apache). If you're using standard settings, your web server is running as user nobody.

If everything is correct, you have a version of MySQL installed on your Freesco-system. You can check the version by typing

mysql -version

If this command gives an error (command not found or something like that), you are not in the right directory to execute the command. The MySQL binaries are installed in /usr/local/mySQL/bin
If you plan to use MySQL regularly, it might be useful to add this directory to your PATH. How to do this is described: here
In this how-to I'll assume that you've done this.

DatabaseName is the name you'll give the database. Example: Myforum_phpBB.
DatabaseAdmin is the username you'll give admin-access to the database: Example: Plop
Password is the password for the DatabaseAdmin. Example: Tekl)S 1)

Make sure you remember the DatabaseName and the user/password combination. You'll need it to set up your phpBB-forum.

Click the 'Finish Installation' and you'll go to the Administration page of your phpBB2 forum where you can set-up your board.
These settings are very well documented in the phpBB manual: http://www.phpbb.com/support/guide/